Geodesic
Lagrangian and $S$ matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 2, pp. 153-160

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Some concrete examples show that there is no direct correlation between the properties of Hermiticity (or locality) of a Lagrangian and uattarity (or causality) of the $S$ matrix in realistic field theories. 
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     author = {B. V. Medvedev and V. P. Pavlov and A. D. Sukhanov},
     title = {Lagrangian and $S$ matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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B. V. Medvedev; V. P. Pavlov; A. D. Sukhanov. Lagrangian and $S$ matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 2, pp. 153-160. http://geodesic.mathdoc.fr/item/TMF_1971_8_2_a0/